Thinking of visiting London this summer? Why not? Okay, it’s expensive. But if it weren’t for the exchange rate — the pound now costs you over two dollars and buys less than one in the only city on earth that makes Manhattan feel cheap — you’d be over here en masse to enjoy our culture, our cuisine, and our glorious new climate. Well, what’s stopping you?

The answer, I suspect, can be summed up in one word: terrorism. You have read enough, not least in this column, about homegrown Islamist terrorists in Britain to scare the pants off any American tourist.

Your TV screens have been filled with footage of my neighbor, Abu Hamza, getting his hooks into untold numbers of scary young fanatics, and you have been told that there are plenty more such preachers, poisoning the receptive minds of what I call the jihadi generation.

Your flesh has been made to creep by revelations of ever more lethal plots, from mass hijacking of trans-Atlantic airliners to radioactive “dirty” bombs. And you saw the threat become reality two years ago, when London buses and subways became scenes of carnage thanks to suicide attacks carried out by young Muslims who are as British as I am.

It is, alas, all true. For Al Qaeda, Britain has been no less important a target than America, but Britain is closer, not only for geographical but also for historical and multicultural reasons, to the front line in Iraq and Afghanistan. Even a global terrorist network requires bases, and increasingly these bases are being discovered right here in Britain.

Only this week, the trial began in London of three men accused of disseminating Al Qaeda propaganda around the world, including beheadings of numerous American, British, and other Western hostages. They also had videos of potential targets in Washington, D.C. One of them, Younis Tsouli, lives in my West London district of Shepherd’s Bush. He is a Moroccan who was given indefinite leave to remain here two months before his arrest. In heaven’s name, why?

Also this week, six men were arrested in London and nearby on charges ranging from incitement to terrorism to providing financial support for terrorist groups abroad. They include Abu Izzadeen, a self-styled imam, who gained notoriety last year by interrupting the live broadcast of a speech by the home secretary, John Reid, in East London, shouting, “How dare you come to a Muslim area when over 1,000 Muslims have been arrested?”

Since then, Mr. Izzadeen has been given ample opportunity by the BBC to reiterate his message that Muslims owe allegiance only to Shariah law, that democracy is against Islam, and that Britain must expect to be attacked for its refusal to surrender to Osama bin Laden. He belongs to an illegal Islamist group known as al-Ghurabaa, the strangers. His real name is Trevor Brooks, and “Abu Izzadeen,” his nom de guerre, means “might of the faith.”

He represents a type of whom we shall, I fear, hear from much more. He was born in London to a Jamaican family, brought up a Christian, but converted to Islam at age 17. He abandoned his trade as an electrician and instead lives on welfare as a full-time agitator. Conversions to radical Islam are increasingly common among young black Britons. I am told by lawyers that in prison, radical Muslims often intimidate young blacks into converting.

Mr. Izzadeen also illustrates another characteristic phenomenon: the legalization of polygamy. His wife is a Palestinian Arab and he has three children, but he recently advertised on the Internet for a “second, third or fourth wife” so that he could have “more than nine children.” Though polygamy is, in theory, illegal, it emerged last week that for decades the Department of Work and Pensions has actually encouraged polygamous Muslims to claim welfare benefits for their additional wives.

There is nothing to stop the likes of Mr. Izzadeen marrying extra wives abroad and returning to Britain to claim welfare for them. The guideline issued by the ministry tells these claimants: “If you were legally married to more than one partner under the laws of a country that permits this, then your relationship is called a polygamous marriage.”

No figures on the numbers of such “polygamous marriages” are available, but the government is, in effect, adding a financial incentive to the religious imperative to take more than one wife.

Now, for some good news. On Tuesday evening, I heard a lecture by the head of Scotland Yard’s Counter Terrorism Command, the deputy assistant commissioner, Peter Clarke. It was a robust warning, both to Muslim communities and to the liberal press. Out of well over 100 prosecutions for terrorism since September 11, he said “few have yet originated from what is sometimes called ‘community intelligence.'” In other words, Muslims are not helping the police to catch terrorists.

Mr. Clarke also warned that Muslim distrust of the police and the intelligence on which they base arrests cannot justify “demands for it to be scrutinized by community representatives, not only after an operation but even before it.” He defended the creation of new offenses and longer detention without charge, however controversial that may be. “The Common Law of England,” he declared, “was not designed to defend us against people who wish to poison or irradiate the public.”

Nor does Mr. Clarke think much of journalists who assume that arrests that do not result in prosecutions are politically motivated. The nature of Islamist terror means that police have to move in before they necessarily have had time to assemble evidence. It takes years before cases come to trial, and even then, reporting restrictions are not always lifted.

The inability to tell the world what is really going on naturally encourages politicians and officials to leak sensitive operational intelligence “to squeeze out some short-term presentational advantage.” For Mr. Clarke, those who do this are “beneath contempt” and “put lives at risk.”

The threat from Al Qaeda is greater than ever — that much is clear. But as long as counterterrorist officers of the caliber of Peter Clarke are allowed to do their jobs, it is safe to come to London.